A bi-level geometrical optimization framework for tailoring kinetostatic behavior of compliant bistable mechanisms

Designing guidance mechanisms using bistable mechanisms with two stable positions is a common low-power solution for maintaining the guidance position without continuous external energy input. However, the coupling between kinematics and statics in compliant bistable mechanisms poses a challenge for their application in mechanism synthesis. To address this issue, this paper introduces the pole similarity transformation theory into the synthesis of compliant mechanisms and proposes a general synthesis method for planar serial-based compliant bistable mechanisms. This method models the compliant mechanism using the strain energy method and analyzes the bistable characteristics of the mechanism within its motion plane using the saddle point searching method. By doing so, the proposed method can identify stable positions without predetermined motion trajectories, making it more suitable for designing compliant bistable mechanisms with general planar motion. Additionally, this method utilizes the pole map to describe the stable positions of the rigid components in the compliant mechanism and establishes an information database for compliant bistable mechanisms. Through leveraging the pole similarity transformation, the pole maps of the mechanisms in the information database are matched with the pole map of the motion task, thus achieving the synthesis of planar serial-based compliant bistable mechanisms for the rigid-body guidance problem. The paper provides a detailed explanation of the mechanism synthesis process and demonstrates its application through a case study.

Abstract. Compliant bistable mechanisms are specialized mechanisms that have specific self-locking characteristics in two positions. They are widely used in aerospace, micro-electromechanical systems, and high-precision manufacturing. The coupling of kinematic with elastomechanical behaviors of compliant mechanisms, known as kinetostatics, increases the difficulty of synthesizing compliant mechanisms. Currently, most research relies on optimization approaches to find compliant mechanisms that meet motion requirements. To address this challenge, this paper proposes a geometric synthesis method for compliant bistable mechanisms to solve the rigid guidance problem. The pole similarity transformation characteristics of planar beams and the static equilibrium characteristic of bistable mechanisms at stable positions are utilized to decouple the kinematic synthesis and static analysis. The proposed method introduces a task-driven synthesis process, where the critical structural parameters in compliant mechanisms are determined based on the desired guidance positions of motion tasks. This approach eliminates the need for a tedious and time-consuming iterative optimization process. The resulting bistable mechanisms have two stable positions that correspond to the desired guidance positions of the motion task. To illustrate the effectiveness of the geometric synthesis method, a two-position problem of a compliant bistable mechanism is provided as an example.

The global push for sustainability and energy efficiency is driving significant advancements across various industries, including the development of electrified solutions for heavy-duty mobile manipulators (HDMMs). Electromechanical linear actuators (EMLAs), powered by permanent magnet synchronous motors, present an all-electric alternative to traditional internal combustion engine (ICE)-powered hydraulic actuators, offering a promising path toward an eco-friendly future for HDMMs. However, the limited operational range of electrified HDMMs, closely tied to battery capacity, highlights the need to fully exploit the potential of EMLAs that drive the manipulators. This goal is contingent upon a deep understanding of the harmonious interplay between EMLA mechanisms and the dynamic behavior of heavy-duty manipulators. To this end, this paper introduces a bilevel multi-objective optimization framework, conceptualizing the EMLA-actuated manipulator of an electrified HDMM as a leader–follower scenario. At the leader level, the optimization algorithm maximizes EMLA efficiency by considering electrical and mechanical constraints, while the follower level optimizes the manipulator’s motion through a trajectory reference generator that adheres to manipulator limits. This optimization approach ensures that the system operates with a synergistic trade-off between the most efficient operating region of the actuation system, achieving a total efficiency of 70.3%. Furthermore, to complement this framework and ensure precise tracking of the generated optimal trajectories, a robust decomposed system control (RDSC) strategy is developed with accurate control and exponential stability. The proposed methodologies are validated on a 3-degrees-of-freedoms (DoFs) manipulator, demonstrating significant efficiency improvements while maintaining high-performance operation. Finally, experiments were conducted on an EMLA test bed under predefined optimal trajectories, simulating the dynamic load conditions of the manipulator’s lift joint and controlled with the developed RDSC. The results validate the effectiveness of the optimization framework and the control strategy.

Support vector machine (SVM) using full features is a common approach for classifying diseases in healthcare systems. However, little literature reported to use it towards determining minimum features of biomarkers. This study introduced a bilevel mixed-integer optimization framework to detect minimum biomarker features for SVM. We proposed the two-population nested hybrid differential evolution (NHDE) to solve the problem. In case studies, two dominant biomarkers were found. The two-population NHDE algorithm was more efficient to achieve minimum biomarkers compared with one-population NHDE and traditional genetic algorithm.

Detection of minimum biomarker features via bi-level optimization framework by nested hybrid differential evolution

Continuum robots have seen increased utilization in various fields such as aerospace, rescue operations, human interaction, and especially medicine. More specifically, in medicine, continuum robots have enabled minimally invasive surgeries and faster patient recovery time. However, the design of continuum robots needs to be improved, especially by enhancing or incorporating characteristics that improve functionality across various applications. This paper explores different mechanisms, including bistable, compliant, and lamina emergent mechanisms, to achieve these design goals. Specifically compliant bistable mechanisms which can store energy when deformed and utilize this energy to transition from one state to another have shown significant promise for the design of continuum robots. In this paper we explore the characteristics and functions associated with compliant bistable mechanisms and their potential integration in device designs, we review the design process for adapting compliant bistable mechanisms to continuum robots, highlighting the challenges and considerations involved. We also present two examples of applications to continuum robot designs that demonstrate the potential of compliant mechanisms for creating varied functionality for a number of applications. By understanding the capabilities and limitations of compliant mechanisms, we can advance the design of continuum robots, which presents a significant opportunity for innovation and progress in the field of medical device design.

A deployable structure can significantly change its geometric shape by switching lattice configurations. Using compliant mechanisms as the lattice units can prevent wear and friction among multi-part mechanisms. This work presents two distinctive deployable structures based on a programmable compliant bistable lattice. Several novel parameters are introduced into the bistable mechanism to better control the behaviour of bistable mechanisms. By adjusting the defined geometry parameters, the programmable bistable lattices can be optimized for specific targets such as a larger deformation range or higher stability. The first structure is designed to perform 1D deployable movement. This structure consists of multi-series-connected bistable lattices. In order to explore the 3D bistable characteristic, a cylindrical deployable mechanism is designed based on the curved double tensural bistable lattice. The investigation of bistable lattices mainly involves four types of bistable mechanisms. These bistable mechanisms are obtained by dividing the long segment of traditional compliant bistable mechanisms into two equal parts and setting a series of angle data to them, respectively. The experiment and FEA simulation results confirm the feasibility of the compliant deployable structures.

In this research a variable-stiffness compliant mechanism was developed to generate variable force-displacement profiles at the mechanism’s coupler point. The mechanism is based on a compliant Robert’s straight-line mechanism, and the stiffness is varied by changing the effective length of the compliant links with an actuated slider. The force-deflection behavior of the mechanism was analyzed using the Pseudo-Rigid Body Model (PRBM), and two key parameters, KΘ and γ, were optimized using finite element analysis (FEA) to match the model with the measured behavior of the mechanism. The variable-stiffness mechanism was used in a one-degree-of-freedom haptic interface (force-feedback device) to demonstrate the effectiveness of varying the stiffness of a compliant mechanism. Unlike traditional haptic interfaces, in which the force is controlled using motors and rigid links, the haptic interface developed in this work displays haptic stiffness via the variable-stiffness compliant mechanism. One of the key features of the mechanism is that the inherent return-to-zero behavior of the compliant mechanism was used to provide the stiffness feedback felt by the user. A prototype haptic interface was developed capable of simulating the force-displacement profile of Lachman’s Test performed on an injured ACL knee. The compliant haptic interface was capable of displaying stiffnesses between 4200 N/m and 7200 N/m.

Heavy-duty commercial electric vehicle (HDEV) charging stations, such as for freight trucks, must handle large peak power demands. Installing on-site energy storage can reduce the peak charging demand to avoid expensive and oversized utility-managed distribution equipment. To ensure optimal design of charging infrastructure, the trade-off between energy storage size and grid equipment ratings should be considered. This paper presents a bi-level multi-objective optimization framework to discover Pareto optimal designs, under the constraint of optimally sized power electronic converters and realistic power loss models. Under these considerations, the bi-level approach can greatly simplify the design process by breaking up charging station optimization into a system-level problem and multiple converter-level problems. Using industry-based HDEV arrival times and charging conditions, this bi-level approach is demonstrated for a 9port charging station. The resulting Pareto front showcases equipment sizing trade-offs that are necessary for informed charging infrastructure development decisions. The bi-level optimization Pareto front is compared the Pareto fronts of traditional, fixed efficiency converter models.

This paper proposes a new class of bistable mechanisms: compliant bistable mechanisms. These mechanisms gain their bistable behavior from the energy stored in the flexible segments which deflect to allow mechanism motion. This approach integrates desired mechanism motion and energy storage to create bistable mechanisms with dramatically reduced part count compared to traditional mechanisms incorporating rigid links, joints, and springs. This paper briefly reviews bistable mechanism theory, introduces some additional bistable mechanism characteristics, and integrates this theory with compliant mechanism theory. The resulting theory of bistable compliant mechanisms is validated by measuring the force and motion characteristics of several test mechanisms and comparing them to predicted values.

Bistable mechanical devices remain stable in two distinct positions without power input. They find application in valves, switches, closures, and clasps. Mechanically bistable behavior results from the storage and release of energy, typically in springs, with stable positions occurring at local minima of stored energy. Compliant mechanisms offer an elegant way to achieve this behavior by incorporating both motion and energy storage into the same flexible element. Interest in compliant bistable mechanisms has also recently increased because of the advantages of bistable behavior in many micro-electro-mechanical systems (MEMS). Design of compliant or rigid-body bistable mechanisms typically requires simultaneous consideration of both energy storage and motion requirements. This paper simplifies this process by developing theory that provides prior knowledge of mechanism configurations that guarantee bistable behavior. Configurations which include one or more translational, or slider, joints are studied in this work. Several different mechanism types are analyzed to determine compliant segment placement that will ensure bistable mechanism operation. Examples demonstrate the power of the theory in design.

In this paper, we present a mathematical approach to synthesize multistable compliant mechanisms by combining multiple bistable equilibrium mechanisms. More specifically, we identify and categorize various types of bistabilities by characterizing the essential elements of their complicated deformation pattern. The behavior of a bistable compliant mechanism, in general, is highly nonlinear. Using combinations of such nonlinearities to capture the behavior of multistable (more than two stable positions) mechanisms can be quite challenging. To determine multistable behavior, our simplified mathematical scheme captures the essential parameters of bistability, such as the load-thresholds that cause the jump to the next stable position. This mathematical simplification enables us to characterize bistable mechanisms by using piecewise lower-order polynomials and, in turn, synthesize multistable mechanisms. Three case studies involving combinations of two, three, and four bistable behaviors are presented for the purpose of generating multistable mechanisms with up to 16 stable positions. The methodology enables us to design a compliant mechanism with a desired number of stable positions. A design example of a quadristable equilibrium rotational compliant mechanism consisting of two bistable submechanisms is presented to demonstrate the effectiveness of the approach.

BackgroundOptimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation.MethodsIn this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock.ResultsOur new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies.

To ensure economic dispatch and suppress cascading failures in hybrid AC/DC power systems, this study proposes a security-aware and cost-effective preventive control strategy based on a bi-level optimization framework. First, given the limitations of existing indicators and simulation methods in accurately characterizing commutation failures, the transient characteristics of such failures are analyzed using electromagnetic transient simulations in PSCAD. A classification approach based on Particle Swarm Optimization–Support Vector Machine (PSO–SVM) is developed to identify and categorize commutation failure scenarios. Then, both system security and economic performance are jointly assessed by considering the AC/DC security margin and total operating cost. A bi-level optimization model is constructed, in which the lower-level optimization model aims to obtain the system security margin, while the upper-level optimization model minimizes the total operational cost. To solve this model and determine the optimal generation dispatch strategy, an Improved Particle Swarm Optimization (IPSO) algorithm is employed. Finally, case studies on a modified IEEE 39-bus system verify the feasibility and effectiveness of the proposed strategy in mitigating cascading failures while achieving economic dispatch in hybrid AC/DC power systems.

From shear centre to eigenwrenches